Geodesic
Integration over a fractal curve and the jump problem
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 549-557.

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A definition of integration, i.e., a generalization of a functional of the form $$ u(z)\mapsto\int_\Gamma f(z)u(z)dz $$ to the case where $\Gamma$ is a fractal curve on the complex plane and $f(z)$ (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined. 
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B. A. Kats. Integration over a fractal curve and the jump problem. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 549-557. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a6/

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